Bernini's Four Rivers fountain in Rome symbolises European rule over the Americas. Photograph: Corbis

Looking at the problems Europe faces today, it is hard to believe this continent once dominated all others. Today, Bernini's Four Rivers fountain in Rome is a spectacular landmark visited by tourists from everywhere. Yet when it was built in the 17th century, the figure of the River Plate on this gorgeous sculptural creation was an image of European rule over the Americas . Four hundred years ago, the rise of Europe seemed as inevitable as its decline may appear today. What were the factors that once made this continent so powerful?

A map of the world created by Martin Waldseemuller in 1507 epitomises that power. On it, Waldseemuller outlines an entire new western continent and names it, for the first time, America. Several things about this map illustrate the success of Europe in its youth. The voyages of discovery that enabled Europeans to name "America" grew out of a culture of genuine curiosity and open thinking, the Renaissance. In Leonardo da Vinci's unfinished painting The Adoration of the Magi there seem to be infinities of figures, infinities of landscape – it pictures a world that is literally limitless. This altarpiece begun a decade before the voyages of Columbus expresses a culture that was ready to see new worlds.

Waldseemuller's map is printed, which makes it the fruit of another revolution of 15th-century Europe. China printed books long before Europeans did but the timing of Europe's print revolution, at the same time that the Renaissance was hungry for new books, and its discoverers were revealing new worlds, was perfect to fuel vibrant change and growth.

Today, crippled by austerity, spooked by debt, Europe is just one continent among others. America and China seem far ahead. Can Europeans ever reclaim the qualities that once made them the most creative people on earth? It is easy to dismiss the achievements of Europe in the past as mere aggressive "imperialism". Yet the empires of Europe were the result, not the cause, of internal leaps forward. European colonialism is thankfully history. Meanwhile, the inner strengths of European culture in the past are self-evident at any great art museum. The Renaissance was just the start. The scientific revolution, the Enlightenment, the French Revolution, liberalism, industry, socialism – all these are European creations. Today the living parts of the European tradition have been globalised. No one thinks of modern science as European in origin – but it is.

Curiosity, cultural ambition, and imagination made Europe great. Can they be unleashed again? European governments desperate to revive growth (our own included) should be trying to kindle a new Renaissance.